|
| |
|
|
A221993
|
|
Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..2 array extended with zeros and convolved with 1,4,6,4,1.
|
|
1
|
|
|
|
2, 3, 4, 6, 10, 15, 22, 36, 56, 84, 133, 208, 318, 495, 772, 1192, 1846, 2870, 4448, 6886, 10686, 16576, 25679, 39819, 61763, 95732, 148415, 230158, 356829, 553197, 857766, 1329946, 2061917, 3196940, 4956807, 7685148, 11915388, 18474452, 28643620
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
|
|
|
LINKS
|
|
|
|
FORMULA
|
Empirical: a(n) = a(n-1) + 3*a(n-3) - 2*a(n-4) - 3*a(n-6) + 2*a(n-7) + a(n-9).
Empirical g.f.: x*(1 + x + x^2)*(2 - x - 3*x^3 + 2*x^4 + x^6) / (1 - x - 3*x^3 + 2*x^4 + 3*x^6 - 2*x^7 - x^9). - Colin Barker, Aug 14 2018
|
|
|
EXAMPLE
|
Some solutions for n=7, one extended zero followed by filtered positions:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....1....1....0....0....1....1....0....1....0....0....0....1
..1....0....0....1....0....0....0....1....0....0....1....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....1....1....0....0
..0....1....0....1....0....0....0....0....1....0....0....0....0....0....0....1
..0....0....1....0....0....0....0....0....0....1....0....0....1....0....0....0
..0....1....0....0....1....0....1....1....0....0....0....0....0....1....0....0
..0....0....0....0....0....0....0....0....0....0....1....1....0....0....0....1
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
